Question

\( \frac{\csc 42^\circ \cdot \cos 37^\circ}{\sec 48^\circ \cdot \sin 53^\circ} \) is:

• A. \( 0 \)
• B. \( \frac{1}{2} \)
• C. \( 1 \)
• D. \( 2 \)

Hint:

Using **reciprocal trigonometric identities** simplifies the fraction.

Answer 1

The Correct Option is B

Using trigonometric identities:
\[ \csc 42^\circ = \frac{1}{\sin 42^\circ}, \quad \sec 48^\circ = \frac{1}{\cos 48^\circ} \] \[ \cos 37^\circ = \sin 53^\circ \] So, \[ \frac{\frac{1}{\sin 42^\circ} \cdot \cos 37^\circ}{\frac{1}{\cos 48^\circ} \cdot \sin 53^\circ} \] \[ = \frac{\cos 37^\circ}{\sin 42^\circ} \times \frac{\cos 48^\circ}{\sin 53^\circ} \] Approximating values,
\[ = \frac{1}{2} \]